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Diffstat (limited to 'src/3rdparty/double-conversion/double-conversion/bignum.cc')
| -rw-r--r-- | src/3rdparty/double-conversion/double-conversion/bignum.cc | 797 |
1 files changed, 797 insertions, 0 deletions
diff --git a/src/3rdparty/double-conversion/double-conversion/bignum.cc b/src/3rdparty/double-conversion/double-conversion/bignum.cc new file mode 100644 index 0000000000..5c74d70d3d --- /dev/null +++ b/src/3rdparty/double-conversion/double-conversion/bignum.cc @@ -0,0 +1,797 @@ +// Copyright 2010 the V8 project authors. All rights reserved. +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// * Redistributions in binary form must reproduce the above +// copyright notice, this list of conditions and the following +// disclaimer in the documentation and/or other materials provided +// with the distribution. +// * Neither the name of Google Inc. nor the names of its +// contributors may be used to endorse or promote products derived +// from this software without specific prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +#include <algorithm> +#include <cstring> + +#include "bignum.h" +#include "utils.h" + +namespace double_conversion { + +Bignum::Chunk& Bignum::RawBigit(const int index) { + DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity); + return bigits_buffer_[index]; +} + + +const Bignum::Chunk& Bignum::RawBigit(const int index) const { + DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity); + return bigits_buffer_[index]; +} + + +template<typename S> +static int BitSize(const S value) { + (void) value; // Mark variable as used. + return 8 * sizeof(value); +} + +// Guaranteed to lie in one Bigit. +void Bignum::AssignUInt16(const uint16_t value) { + DOUBLE_CONVERSION_ASSERT(kBigitSize >= BitSize(value)); + Zero(); + if (value > 0) { + RawBigit(0) = value; + used_bigits_ = 1; + } +} + + +void Bignum::AssignUInt64(uint64_t value) { + Zero(); + for(int i = 0; value > 0; ++i) { + RawBigit(i) = value & kBigitMask; + value >>= kBigitSize; + ++used_bigits_; + } +} + + +void Bignum::AssignBignum(const Bignum& other) { + exponent_ = other.exponent_; + for (int i = 0; i < other.used_bigits_; ++i) { + RawBigit(i) = other.RawBigit(i); + } + used_bigits_ = other.used_bigits_; +} + + +static uint64_t ReadUInt64(const Vector<const char> buffer, + const int from, + const int digits_to_read) { + uint64_t result = 0; + for (int i = from; i < from + digits_to_read; ++i) { + const int digit = buffer[i] - '0'; + DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9); + result = result * 10 + digit; + } + return result; +} + + +void Bignum::AssignDecimalString(const Vector<const char> value) { + // 2^64 = 18446744073709551616 > 10^19 + static const int kMaxUint64DecimalDigits = 19; + Zero(); + int length = value.length(); + unsigned pos = 0; + // Let's just say that each digit needs 4 bits. + while (length >= kMaxUint64DecimalDigits) { + const uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); + pos += kMaxUint64DecimalDigits; + length -= kMaxUint64DecimalDigits; + MultiplyByPowerOfTen(kMaxUint64DecimalDigits); + AddUInt64(digits); + } + const uint64_t digits = ReadUInt64(value, pos, length); + MultiplyByPowerOfTen(length); + AddUInt64(digits); + Clamp(); +} + + +static uint64_t HexCharValue(const int c) { + if ('0' <= c && c <= '9') { + return c - '0'; + } + if ('a' <= c && c <= 'f') { + return 10 + c - 'a'; + } + DOUBLE_CONVERSION_ASSERT('A' <= c && c <= 'F'); + return 10 + c - 'A'; +} + + +// Unlike AssignDecimalString(), this function is "only" used +// for unit-tests and therefore not performance critical. +void Bignum::AssignHexString(Vector<const char> value) { + Zero(); + // Required capacity could be reduced by ignoring leading zeros. + EnsureCapacity(((value.length() * 4) + kBigitSize - 1) / kBigitSize); + DOUBLE_CONVERSION_ASSERT(sizeof(uint64_t) * 8 >= kBigitSize + 4); // TODO: static_assert + // Accumulates converted hex digits until at least kBigitSize bits. + // Works with non-factor-of-four kBigitSizes. + uint64_t tmp = 0; + for (int cnt = 0; !value.is_empty(); value.pop_back()) { + tmp |= (HexCharValue(value.last()) << cnt); + if ((cnt += 4) >= kBigitSize) { + RawBigit(used_bigits_++) = (tmp & kBigitMask); + cnt -= kBigitSize; + tmp >>= kBigitSize; + } + } + if (tmp > 0) { + DOUBLE_CONVERSION_ASSERT(tmp <= kBigitMask); + RawBigit(used_bigits_++) = static_cast<Bignum::Chunk>(tmp & kBigitMask); + } + Clamp(); +} + + +void Bignum::AddUInt64(const uint64_t operand) { + if (operand == 0) { + return; + } + Bignum other; + other.AssignUInt64(operand); + AddBignum(other); +} + + +void Bignum::AddBignum(const Bignum& other) { + DOUBLE_CONVERSION_ASSERT(IsClamped()); + DOUBLE_CONVERSION_ASSERT(other.IsClamped()); + + // If this has a greater exponent than other append zero-bigits to this. + // After this call exponent_ <= other.exponent_. + Align(other); + + // There are two possibilities: + // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) + // bbbbb 00000000 + // ---------------- + // ccccccccccc 0000 + // or + // aaaaaaaaaa 0000 + // bbbbbbbbb 0000000 + // ----------------- + // cccccccccccc 0000 + // In both cases we might need a carry bigit. + + EnsureCapacity(1 + (std::max)(BigitLength(), other.BigitLength()) - exponent_); + Chunk carry = 0; + int bigit_pos = other.exponent_ - exponent_; + DOUBLE_CONVERSION_ASSERT(bigit_pos >= 0); + for (int i = used_bigits_; i < bigit_pos; ++i) { + RawBigit(i) = 0; + } + for (int i = 0; i < other.used_bigits_; ++i) { + const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0; + const Chunk sum = my + other.RawBigit(i) + carry; + RawBigit(bigit_pos) = sum & kBigitMask; + carry = sum >> kBigitSize; + ++bigit_pos; + } + while (carry != 0) { + const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0; + const Chunk sum = my + carry; + RawBigit(bigit_pos) = sum & kBigitMask; + carry = sum >> kBigitSize; + ++bigit_pos; + } + used_bigits_ = static_cast<int16_t>(std::max(bigit_pos, static_cast<int>(used_bigits_))); + DOUBLE_CONVERSION_ASSERT(IsClamped()); +} + + +void Bignum::SubtractBignum(const Bignum& other) { + DOUBLE_CONVERSION_ASSERT(IsClamped()); + DOUBLE_CONVERSION_ASSERT(other.IsClamped()); + // We require this to be bigger than other. + DOUBLE_CONVERSION_ASSERT(LessEqual(other, *this)); + + Align(other); + + const int offset = other.exponent_ - exponent_; + Chunk borrow = 0; + int i; + for (i = 0; i < other.used_bigits_; ++i) { + DOUBLE_CONVERSION_ASSERT((borrow == 0) || (borrow == 1)); + const Chunk difference = RawBigit(i + offset) - other.RawBigit(i) - borrow; + RawBigit(i + offset) = difference & kBigitMask; + borrow = difference >> (kChunkSize - 1); + } + while (borrow != 0) { + const Chunk difference = RawBigit(i + offset) - borrow; + RawBigit(i + offset) = difference & kBigitMask; + borrow = difference >> (kChunkSize - 1); + ++i; + } + Clamp(); +} + + +void Bignum::ShiftLeft(const int shift_amount) { + if (used_bigits_ == 0) { + return; + } + exponent_ += static_cast<int16_t>(shift_amount / kBigitSize); + const int local_shift = shift_amount % kBigitSize; + EnsureCapacity(used_bigits_ + 1); + BigitsShiftLeft(local_shift); +} + + +void Bignum::MultiplyByUInt32(const uint32_t factor) { + if (factor == 1) { + return; + } + if (factor == 0) { + Zero(); + return; + } + if (used_bigits_ == 0) { + return; + } + // The product of a bigit with the factor is of size kBigitSize + 32. + // Assert that this number + 1 (for the carry) fits into double chunk. + DOUBLE_CONVERSION_ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); + DoubleChunk carry = 0; + for (int i = 0; i < used_bigits_; ++i) { + const DoubleChunk product = static_cast<DoubleChunk>(factor) * RawBigit(i) + carry; + RawBigit(i) = static_cast<Chunk>(product & kBigitMask); + carry = (product >> kBigitSize); + } + while (carry != 0) { + EnsureCapacity(used_bigits_ + 1); + RawBigit(used_bigits_) = carry & kBigitMask; + used_bigits_++; + carry >>= kBigitSize; + } +} + + +void Bignum::MultiplyByUInt64(const uint64_t factor) { + if (factor == 1) { + return; + } + if (factor == 0) { + Zero(); + return; + } + if (used_bigits_ == 0) { + return; + } + DOUBLE_CONVERSION_ASSERT(kBigitSize < 32); + uint64_t carry = 0; + const uint64_t low = factor & 0xFFFFFFFF; + const uint64_t high = factor >> 32; + for (int i = 0; i < used_bigits_; ++i) { + const uint64_t product_low = low * RawBigit(i); + const uint64_t product_high = high * RawBigit(i); + const uint64_t tmp = (carry & kBigitMask) + product_low; + RawBigit(i) = tmp & kBigitMask; + carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + + (product_high << (32 - kBigitSize)); + } + while (carry != 0) { + EnsureCapacity(used_bigits_ + 1); + RawBigit(used_bigits_) = carry & kBigitMask; + used_bigits_++; + carry >>= kBigitSize; + } +} + + +void Bignum::MultiplyByPowerOfTen(const int exponent) { + static const uint64_t kFive27 = DOUBLE_CONVERSION_UINT64_2PART_C(0x6765c793, fa10079d); + static const uint16_t kFive1 = 5; + static const uint16_t kFive2 = kFive1 * 5; + static const uint16_t kFive3 = kFive2 * 5; + static const uint16_t kFive4 = kFive3 * 5; + static const uint16_t kFive5 = kFive4 * 5; + static const uint16_t kFive6 = kFive5 * 5; + static const uint32_t kFive7 = kFive6 * 5; + static const uint32_t kFive8 = kFive7 * 5; + static const uint32_t kFive9 = kFive8 * 5; + static const uint32_t kFive10 = kFive9 * 5; + static const uint32_t kFive11 = kFive10 * 5; + static const uint32_t kFive12 = kFive11 * 5; + static const uint32_t kFive13 = kFive12 * 5; + static const uint32_t kFive1_to_12[] = + { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, + kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; + + DOUBLE_CONVERSION_ASSERT(exponent >= 0); + + if (exponent == 0) { + return; + } + if (used_bigits_ == 0) { + return; + } + // We shift by exponent at the end just before returning. + int remaining_exponent = exponent; + while (remaining_exponent >= 27) { + MultiplyByUInt64(kFive27); + remaining_exponent -= 27; + } + while (remaining_exponent >= 13) { + MultiplyByUInt32(kFive13); + remaining_exponent -= 13; + } + if (remaining_exponent > 0) { + MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); + } + ShiftLeft(exponent); +} + + +void Bignum::Square() { + DOUBLE_CONVERSION_ASSERT(IsClamped()); + const int product_length = 2 * used_bigits_; + EnsureCapacity(product_length); + + // Comba multiplication: compute each column separately. + // Example: r = a2a1a0 * b2b1b0. + // r = 1 * a0b0 + + // 10 * (a1b0 + a0b1) + + // 100 * (a2b0 + a1b1 + a0b2) + + // 1000 * (a2b1 + a1b2) + + // 10000 * a2b2 + // + // In the worst case we have to accumulate nb-digits products of digit*digit. + // + // Assert that the additional number of bits in a DoubleChunk are enough to + // sum up used_digits of Bigit*Bigit. + if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_bigits_) { + DOUBLE_CONVERSION_UNIMPLEMENTED(); + } + DoubleChunk accumulator = 0; + // First shift the digits so we don't overwrite them. + const int copy_offset = used_bigits_; + for (int i = 0; i < used_bigits_; ++i) { + RawBigit(copy_offset + i) = RawBigit(i); + } + // We have two loops to avoid some 'if's in the loop. + for (int i = 0; i < used_bigits_; ++i) { + // Process temporary digit i with power i. + // The sum of the two indices must be equal to i. + int bigit_index1 = i; + int bigit_index2 = 0; + // Sum all of the sub-products. + while (bigit_index1 >= 0) { + const Chunk chunk1 = RawBigit(copy_offset + bigit_index1); + const Chunk chunk2 = RawBigit(copy_offset + bigit_index2); + accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; + bigit_index1--; + bigit_index2++; + } + RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask; + accumulator >>= kBigitSize; + } + for (int i = used_bigits_; i < product_length; ++i) { + int bigit_index1 = used_bigits_ - 1; + int bigit_index2 = i - bigit_index1; + // Invariant: sum of both indices is again equal to i. + // Inner loop runs 0 times on last iteration, emptying accumulator. + while (bigit_index2 < used_bigits_) { + const Chunk chunk1 = RawBigit(copy_offset + bigit_index1); + const Chunk chunk2 = RawBigit(copy_offset + bigit_index2); + accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; + bigit_index1--; + bigit_index2++; + } + // The overwritten RawBigit(i) will never be read in further loop iterations, + // because bigit_index1 and bigit_index2 are always greater + // than i - used_bigits_. + RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask; + accumulator >>= kBigitSize; + } + // Since the result was guaranteed to lie inside the number the + // accumulator must be 0 now. + DOUBLE_CONVERSION_ASSERT(accumulator == 0); + + // Don't forget to update the used_digits and the exponent. + used_bigits_ = static_cast<int16_t>(product_length); + exponent_ *= 2; + Clamp(); +} + + +void Bignum::AssignPowerUInt16(uint16_t base, const int power_exponent) { + DOUBLE_CONVERSION_ASSERT(base != 0); + DOUBLE_CONVERSION_ASSERT(power_exponent >= 0); + if (power_exponent == 0) { + AssignUInt16(1); + return; + } + Zero(); + int shifts = 0; + // We expect base to be in range 2-32, and most often to be 10. + // It does not make much sense to implement different algorithms for counting + // the bits. + while ((base & 1) == 0) { + base >>= 1; + shifts++; + } + int bit_size = 0; + int tmp_base = base; + while (tmp_base != 0) { + tmp_base >>= 1; + bit_size++; + } + const int final_size = bit_size * power_exponent; + // 1 extra bigit for the shifting, and one for rounded final_size. + EnsureCapacity(final_size / kBigitSize + 2); + + // Left to Right exponentiation. + int mask = 1; + while (power_exponent >= mask) mask <<= 1; + + // The mask is now pointing to the bit above the most significant 1-bit of + // power_exponent. + // Get rid of first 1-bit; + mask >>= 2; + uint64_t this_value = base; + + bool delayed_multiplication = false; + const uint64_t max_32bits = 0xFFFFFFFF; + while (mask != 0 && this_value <= max_32bits) { + this_value = this_value * this_value; + // Verify that there is enough space in this_value to perform the + // multiplication. The first bit_size bits must be 0. + if ((power_exponent & mask) != 0) { + DOUBLE_CONVERSION_ASSERT(bit_size > 0); + const uint64_t base_bits_mask = + ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); + const bool high_bits_zero = (this_value & base_bits_mask) == 0; + if (high_bits_zero) { + this_value *= base; + } else { + delayed_multiplication = true; + } + } + mask >>= 1; + } + AssignUInt64(this_value); + if (delayed_multiplication) { + MultiplyByUInt32(base); + } + + // Now do the same thing as a bignum. + while (mask != 0) { + Square(); + if ((power_exponent & mask) != 0) { + MultiplyByUInt32(base); + } + mask >>= 1; + } + + // And finally add the saved shifts. + ShiftLeft(shifts * power_exponent); +} + + +// Precondition: this/other < 16bit. +uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { + DOUBLE_CONVERSION_ASSERT(IsClamped()); + DOUBLE_CONVERSION_ASSERT(other.IsClamped()); + DOUBLE_CONVERSION_ASSERT(other.used_bigits_ > 0); + + // Easy case: if we have less digits than the divisor than the result is 0. + // Note: this handles the case where this == 0, too. + if (BigitLength() < other.BigitLength()) { + return 0; + } + + Align(other); + + uint16_t result = 0; + + // Start by removing multiples of 'other' until both numbers have the same + // number of digits. + while (BigitLength() > other.BigitLength()) { + // This naive approach is extremely inefficient if `this` divided by other + // is big. This function is implemented for doubleToString where + // the result should be small (less than 10). + DOUBLE_CONVERSION_ASSERT(other.RawBigit(other.used_bigits_ - 1) >= ((1 << kBigitSize) / 16)); + DOUBLE_CONVERSION_ASSERT(RawBigit(used_bigits_ - 1) < 0x10000); + // Remove the multiples of the first digit. + // Example this = 23 and other equals 9. -> Remove 2 multiples. + result += static_cast<uint16_t>(RawBigit(used_bigits_ - 1)); + SubtractTimes(other, RawBigit(used_bigits_ - 1)); + } + + DOUBLE_CONVERSION_ASSERT(BigitLength() == other.BigitLength()); + + // Both bignums are at the same length now. + // Since other has more than 0 digits we know that the access to + // RawBigit(used_bigits_ - 1) is safe. + const Chunk this_bigit = RawBigit(used_bigits_ - 1); + const Chunk other_bigit = other.RawBigit(other.used_bigits_ - 1); + + if (other.used_bigits_ == 1) { + // Shortcut for easy (and common) case. + int quotient = this_bigit / other_bigit; + RawBigit(used_bigits_ - 1) = this_bigit - other_bigit * quotient; + DOUBLE_CONVERSION_ASSERT(quotient < 0x10000); + result += static_cast<uint16_t>(quotient); + Clamp(); + return result; + } + + const int division_estimate = this_bigit / (other_bigit + 1); + DOUBLE_CONVERSION_ASSERT(division_estimate < 0x10000); + result += static_cast<uint16_t>(division_estimate); + SubtractTimes(other, division_estimate); + + if (other_bigit * (division_estimate + 1) > this_bigit) { + // No need to even try to subtract. Even if other's remaining digits were 0 + // another subtraction would be too much. + return result; + } + + while (LessEqual(other, *this)) { + SubtractBignum(other); + result++; + } + return result; +} + + +template<typename S> +static int SizeInHexChars(S number) { + DOUBLE_CONVERSION_ASSERT(number > 0); + int result = 0; + while (number != 0) { + number >>= 4; + result++; + } + return result; +} + + +static char HexCharOfValue(const int value) { + DOUBLE_CONVERSION_ASSERT(0 <= value && value <= 16); + if (value < 10) { + return static_cast<char>(value + '0'); + } + return static_cast<char>(value - 10 + 'A'); +} + + +bool Bignum::ToHexString(char* buffer, const int buffer_size) const { + DOUBLE_CONVERSION_ASSERT(IsClamped()); + // Each bigit must be printable as separate hex-character. + DOUBLE_CONVERSION_ASSERT(kBigitSize % 4 == 0); + static const int kHexCharsPerBigit = kBigitSize / 4; + + if (used_bigits_ == 0) { + if (buffer_size < 2) { + return false; + } + buffer[0] = '0'; + buffer[1] = '\0'; + return true; + } + // We add 1 for the terminating '\0' character. + const int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + + SizeInHexChars(RawBigit(used_bigits_ - 1)) + 1; + if (needed_chars > buffer_size) { + return false; + } + int string_index = needed_chars - 1; + buffer[string_index--] = '\0'; + for (int i = 0; i < exponent_; ++i) { + for (int j = 0; j < kHexCharsPerBigit; ++j) { + buffer[string_index--] = '0'; + } + } + for (int i = 0; i < used_bigits_ - 1; ++i) { + Chunk current_bigit = RawBigit(i); + for (int j = 0; j < kHexCharsPerBigit; ++j) { + buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); + current_bigit >>= 4; + } + } + // And finally the last bigit. + Chunk most_significant_bigit = RawBigit(used_bigits_ - 1); + while (most_significant_bigit != 0) { + buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); + most_significant_bigit >>= 4; + } + return true; +} + + +Bignum::Chunk Bignum::BigitOrZero(const int index) const { + if (index >= BigitLength()) { + return 0; + } + if (index < exponent_) { + return 0; + } + return RawBigit(index - exponent_); +} + + +int Bignum::Compare(const Bignum& a, const Bignum& b) { + DOUBLE_CONVERSION_ASSERT(a.IsClamped()); + DOUBLE_CONVERSION_ASSERT(b.IsClamped()); + const int bigit_length_a = a.BigitLength(); + const int bigit_length_b = b.BigitLength(); + if (bigit_length_a < bigit_length_b) { + return -1; + } + if (bigit_length_a > bigit_length_b) { + return +1; + } + for (int i = bigit_length_a - 1; i >= (std::min)(a.exponent_, b.exponent_); --i) { + const Chunk bigit_a = a.BigitOrZero(i); + const Chunk bigit_b = b.BigitOrZero(i); + if (bigit_a < bigit_b) { + return -1; + } + if (bigit_a > bigit_b) { + return +1; + } + // Otherwise they are equal up to this digit. Try the next digit. + } + return 0; +} + + +int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { + DOUBLE_CONVERSION_ASSERT(a.IsClamped()); + DOUBLE_CONVERSION_ASSERT(b.IsClamped()); + DOUBLE_CONVERSION_ASSERT(c.IsClamped()); + if (a.BigitLength() < b.BigitLength()) { + return PlusCompare(b, a, c); + } + if (a.BigitLength() + 1 < c.BigitLength()) { + return -1; + } + if (a.BigitLength() > c.BigitLength()) { + return +1; + } + // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than + // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one + // of 'a'. + if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { + return -1; + } + + Chunk borrow = 0; + // Starting at min_exponent all digits are == 0. So no need to compare them. + const int min_exponent = (std::min)((std::min)(a.exponent_, b.exponent_), c.exponent_); + for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { + const Chunk chunk_a = a.BigitOrZero(i); + const Chunk chunk_b = b.BigitOrZero(i); + const Chunk chunk_c = c.BigitOrZero(i); + const Chunk sum = chunk_a + chunk_b; + if (sum > chunk_c + borrow) { + return +1; + } else { + borrow = chunk_c + borrow - sum; + if (borrow > 1) { + return -1; + } + borrow <<= kBigitSize; + } + } + if (borrow == 0) { + return 0; + } + return -1; +} + + +void Bignum::Clamp() { + while (used_bigits_ > 0 && RawBigit(used_bigits_ - 1) == 0) { + used_bigits_--; + } + if (used_bigits_ == 0) { + // Zero. + exponent_ = 0; + } +} + + +void Bignum::Align(const Bignum& other) { + if (exponent_ > other.exponent_) { + // If "X" represents a "hidden" bigit (by the exponent) then we are in the + // following case (a == this, b == other): + // a: aaaaaaXXXX or a: aaaaaXXX + // b: bbbbbbX b: bbbbbbbbXX + // We replace some of the hidden digits (X) of a with 0 digits. + // a: aaaaaa000X or a: aaaaa0XX + const int zero_bigits = exponent_ - other.exponent_; + EnsureCapacity(used_bigits_ + zero_bigits); + for (int i = used_bigits_ - 1; i >= 0; --i) { + RawBigit(i + zero_bigits) = RawBigit(i); + } + for (int i = 0; i < zero_bigits; ++i) { + RawBigit(i) = 0; + } + used_bigits_ += static_cast<int16_t>(zero_bigits); + exponent_ -= static_cast<int16_t>(zero_bigits); + + DOUBLE_CONVERSION_ASSERT(used_bigits_ >= 0); + DOUBLE_CONVERSION_ASSERT(exponent_ >= 0); + } +} + + +void Bignum::BigitsShiftLeft(const int shift_amount) { + DOUBLE_CONVERSION_ASSERT(shift_amount < kBigitSize); + DOUBLE_CONVERSION_ASSERT(shift_amount >= 0); + Chunk carry = 0; + for (int i = 0; i < used_bigits_; ++i) { + const Chunk new_carry = RawBigit(i) >> (kBigitSize - shift_amount); + RawBigit(i) = ((RawBigit(i) << shift_amount) + carry) & kBigitMask; + carry = new_carry; + } + if (carry != 0) { + RawBigit(used_bigits_) = carry; + used_bigits_++; + } +} + + +void Bignum::SubtractTimes(const Bignum& other, const int factor) { + DOUBLE_CONVERSION_ASSERT(exponent_ <= other.exponent_); + if (factor < 3) { + for (int i = 0; i < factor; ++i) { + SubtractBignum(other); + } + return; + } + Chunk borrow = 0; + const int exponent_diff = other.exponent_ - exponent_; + for (int i = 0; i < other.used_bigits_; ++i) { + const DoubleChunk product = static_cast<DoubleChunk>(factor) * other.RawBigit(i); + const DoubleChunk remove = borrow + product; + const Chunk difference = RawBigit(i + exponent_diff) - (remove & kBigitMask); + RawBigit(i + exponent_diff) = difference & kBigitMask; + borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + + (remove >> kBigitSize)); + } + for (int i = other.used_bigits_ + exponent_diff; i < used_bigits_; ++i) { + if (borrow == 0) { + return; + } + const Chunk difference = RawBigit(i) - borrow; + RawBigit(i) = difference & kBigitMask; + borrow = difference >> (kChunkSize - 1); + } + Clamp(); +} + + +} // namespace double_conversion |